Re: problems with classical physics

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Leigh's comments about my example of the problem of infinite
entropies in classical stat mech.
> ...
> > ...
> > Also, all physical *entropies would be infinite* since in any finite
> > region of phase space, no matter how small, there are a continuously
> > infinite number of microscopic states in classical mechanics....
>
> I think this should not be construed as an unresolved issue.

I hope others did not think I mean to construe it as an unresolved issue.
I meant to use it as an example of a "problem ... with classical
physics".

>                                                              The only
> contribution that quantum mechanics makes to thermodynamics is that
> it permits the explanation of thermodynamic values, like the entropy,
> of systems which have important nonclassical quantum statistical
> contributions to consider. The finite nature of a cell in phase space
> is needed only conceptually; its size is never an issue. At the turn
> of the century only entropy *changes* were considered to be physical,
> and these are (and were?) readily explained without knowing the
> specific cell volume.

The use of a finite cell volume in phase space in classical stat mech
is a classical version of a type of divergence "regularization" scheme
(most famous examples come from quantum field theory) where a theory
predicts a divergence in some quantity/ies (but one which has only
*differences* in it/them as operationally measurable) is tamed by
artificially restricting the theory in a way that prevents an
asymptotic limit (which causes the divergence/s) from being taken, and
after the finitely measurable quantities are calculated, then the
asymototic limit is either allowed to be taken or its necessity to do
so becomes irrelevant in practice.

It is the finite (nonzero) value of h-bar that makes classical stat mech
into a "finite" theory.  Without that finiteness classical stat mech is
merely a "regularizable" (like being renormalizable in quantum field
theory) theory.  In thermodynamics one can only operationally measure
thermodynamic entropy differences, so whether or not an infinite constant
is present in the actual value of the entropies considered becomes
irrelevant for physical measurements.  But it is not irrelevant for the
conceptual meaning of what entropy actually *is*.

Also, it is a fact that the subtraction of that infinite constant from
the entropy (done to make the theory finite) causes the third law of
thermodynamics to be violated in classical stat mech as a consequence
of that subtraction (not to mention the problem of interpreting the info
theoretic meaning of the negative entropy that any thermodynamic system
must give at sufficiently low temperatures). Classical stat mech *must*
disagree with experimentally measurable results (e.g., consider the
behavior of the specific heat) at sufficiently low temperatures for any
thermodynamic system, no matter how "classically" it behaves at
sufficiently high temperatures.

David Bowman
David_Bowman@georgetowncollege.edu